
Here \(\gamma =1/\sqrt{1-\mathcal {V}^2}\)  is the Lorentz factor. The centripetal acceleration is given by
\(a=\mathcal {V}^2\gamma ^2/R\) , which will provide a length scale in the dynamics. The atoms are
weakly coupled with the external quantum fields. The distance between the atoms is taken to be
smaller than the correlation length of the field. Total Hamiltonian of the system+field is written
as [1]},
\(\mathcal {H}= \mathcal {H}_s+\mathcal {H}_f+\mathcal {H}_{sf}~.\nonumber \) 
